Finite Group Databasebeta

← C₇⋊#168 #63298

Subgroups — C₇⋊#168 #63298

Order 280.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₇	C₄	1	1	yes	characteristic
3	C₇⋊C₈	—	5	1	no	maximal, Hall
4	#168	—	7	1	no	maximal, Hall
5	C₅×C₇	C₈	1	1	yes	characteristic, complemented, Hall
6	C₄×C₇	D₅	1	1	yes	characteristic
7	C₄×C₅	D₇	1	1	yes	characteristic
8	C₂×C₇	Dic₅	1	1	yes	characteristic
9	C₂×C₅	Dic₇	1	1	yes	characteristic
10	C₈	—	35	1	no	Sylow
11	C₇	#168	1	1	yes	characteristic, complemented, Sylow
12	C₅	C₇⋊C₈	1	1	yes	characteristic, complemented, Sylow
13	C₄	D₃₅	1	1	yes	characteristic
14	C₂	Dic₃₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃₅
commutator, hypocenter	C₅×C₇	C₈
Fitting, cosocle	C₄×C₅×C₇	C₂
socle, prime radical	C₂×C₅×C₇	C₄
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₅×C₇	C₈	semidirect
11. C₇	#168	semidirect
12. C₅	C₇⋊C₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₅×C₇	2
C₇⋊C₈	5
#168	7